At the risk of sounding like I'm teaching you to suck eggs, you would be well advised to obtain a copy of the workshop manual. I've removed these dozens of times. The main thing is to ensure you orientate everything correctly.
Feed the lock barrel through the seat panel (as you are aware the tabs on the lock barrel are different sizes and will only pass through the panel one way due to the asymmetric slots) and place the cable bracket over the barrel from the inside. It will only go on one way since the slots on the bracket should correspond with the asymmetric plastic tabs on the lock barrel. Screw on and tighten the plastic nut down onto the bracket, hand tight then a half turn will suffice. Ensure flat face of nut is NOT uppermost. Insert spring so that one end fits into the corresponding hole in the barrel body. Hook the end of the cable into the actuating arm. Attach the actuating arm to the barrel, whilst you hook the other end of the spring into the hole within it. Fit the domed spring washer (dome side up) and tighten the fastening screw over the top.
The orientation of the arm is the all important part here. You need to position it so that with the key out of the lock, the arm is not pulling on the cable, but is held in this rest position by the spring. On insertion of the key the arm needs to rotate anticlockwise against this spring to pull on the cable and release the seat lock. On releasing pressure on the key, the spring should rotate the arm clockwise to return it to the previous position. Here's a picture of the lock on my previous 1199 which shows the orientation of the arm. Sorry its not the best of pictures, as the forum wont let me upload any larger more detailed images. (Mods, is this issue being addressed BTW?). Hope this helps.